ABSTRACT
There is a need for efficient modeling strategies which quickly lead to reliable mathematical models that can be applied for design and optimization of (bio)-chemical processes. The serial gray box modeling strategy is potentially very efficient because no detailed knowledge is needed to construct the white box part of the model and because covenient black box modeling techniques like neural networks can be used for the black box part of the model. This paper shows for a typical biochemical conversion how the serial gray box modeling strategy can be applied efficiently to obtain a model with good frequency extrapolation properties. Models with good frequency extrapolation properties can be applied under dynamic conditions that were not present during the identification experiments. For a given application domain of a model, this property can be used to considerably reduce the number of identification experiments. The serial gray box modeling strategy is demonstrated to be successful for the modeling of the enzymatic conversion of penicillin G In the concentration range of 10-100 mM and temperature range of 298-335 K. Frequency extrapolation is shown by using only constant temperatures in the (batch) identification experiments, while the model can be used reliable with varying temperatures during the (batch) validation experiments. No reliable frequency extrapolation properties could be obtained for a black box model, and for a more knowledge-driven white box model reliable frequency extrapolation properties could only be obtained by incorporating more knowledge in the model. Copyright 1999 John Wiley & Sons, Inc.
